High Resistance MeasurementUpdated 30 January 2025![]()
Fertiliser Resistivity-Probe
IntroductionThe photo above shows a Resistivity-Probe for measuring the resistivity of granular fertiliser. Resistivity is defined below as the resistance observed, times a cell constant. The cell constant is the area of one electrode divided by the spacing between the two electrodes. A 2,150,000,000 ohm resistor (2.15 Gig-ohm or 2.15E9 ohms) is used for calibration. This resistor is in turn calibrated using a measured 10,000,000 ohm 1% resistor (10 Megohms or 1E7 ohms) as a reference. The design could be adapted for many other applications. With powdered or granular materials the electrodes are almost completely inserted into the sample. The switch is then turned on. After a delay the LED might light up. The delay time is proportional to the resistance of the sample as measured by the electrodes. Features
PrincipleOne of the electrodes is connected to a 10 nanofarad current-integrating capacitor via a 1E7 ohm resistor. This resistor has a much lower value than a typical measured resistance. It simply protects the circuit. The other electrode connects to +3 volts. A 3 volt 200 mA hour CR2032 lithium cell powers the circuit via a switch. If the sample is slightly conductive, a current passes between the electrodes into the 10 nanofarad integrating capacitor. When the charge on the capacitor reaches a fixed fraction of the applied voltage, the green/white LED will turn on. The time taken for the LED to turn on is proportional to the resistance of the sample. The standard resistance of 2.15E9 ohms, connected to the electrodes, will take about 19.5 seconds to turn the LED on. This time will vary slightly, between circuits, because of component tolerances. Measuring the highest resistances with a meter would require some shielding from external electrical noise. An integrator performs better. ![]()
Fertiliser Resistivity-Probe Circuit
The circuit above gives an indication of the design. The unmarked devices are two Schmitt triggers and one white/green LED. There is also a 100 nF capacitor across the 3 volt power supply to the Schmitt triggers. The insulation of the box and the circuit has to be many times better than what is being measured. Parts of the final circuit needed special insulation techniques. At 300 micro amps (LED on) the battery life should be 200 mA hour / 0.3 mA = 666 hours. With the LED off, and the power turned on, the battery life = 200 mA hour / 0.01 mA = 20,000 hours. Since the circuit is normally not run continuously, the battery life should be close to its shelf life. Using the Resistivity-ProbeMy resistance standard has a resistance of 2.15E9 ohms. The Resistivity-Probe is connected to the 2.15E9 ohm standard resistor and turned on. The integration time, until the LED is illuminated, is 19.5 seconds. Insert the probe to nearly the full depth into the sample and turn it on. The case surface between the probes, should not be contaminated by the sample. The sample is preferably in a granular or a powdered state. The probe is used to compare samples with similar preparations. Use a timer to measure the delay until the LED turns on. This delay in seconds is proportional to the resistivity of the sample. Allow the electronics to settle for about a minute after turning off, before the next reading. Even better, when the Resistivity-Probe is turned off, simply short the two probes by touching both to the ground. A finger or a paper clip would serve the same purpose. A sample with an integration time of 100 seconds has a resistance of (2.15E9 ohms / 19.5 seconds) x 100 seconds = 1.10E10 ohms. A logical check shows: (standard ohms / standard seconds) x sample seconds = sample ohms. Everything cancels except sample and ohms. Resistivity can be estimated by multiplying the observed resistance by the cell constant of 0.2 metre. Resistivity = 1.10E10 x 0.2 = 2.2E9 ohm metre. ResistivityFor bulk samples the resistance measured is expressed as resistivity. Resistivity = resistance x electrode area / electrode spacing. Resistivity is a bulk property which is independent of the electrode geometry. The electrode area / electrode spacing is called the cell constant. The cell constant unit is metre2/metre = metre. Resistivity has a unit of ohm metre. For safe handling of some powdered or granulated samples an upper resistivity limit is set, 1E9 ohm metre for example. Above this value fires or clogging could occur during sample handling. For the Resistivity-Probe the cell constant is approximately 0.2 metre. At the resistivity limit the resistance measured is 1E9 / 0.2 = 5E9 ohms. The Integration time for this resistance is = 19.5 / 2.15E9 x 5E9 = 45 seconds. Cell ConstantThe cell constant would be easier to calculate if each probe had one flat rectangular face. Measuring the area of one electrode (metre 2) and dividing by the separation (metre) would directly yield the cell constant (metre). I measured the 1 kHz AC resistance of partly distilled water using two probes mounted in a small bath. I used a 1 kHz Wheatstone Bridge for this measurement. I measured the same water sample between some flat electrodes of a known area and separation, again using the 1 kHz Wheatstone Bridge. This allowed me to calculate the Resistivity-Probe cell constant of 0.260 metre. There are probably some polarisation effects to take into account. I don't have the standard platinum-black electrodes used for precision conductivity measurements. Looking at the probe dimensions and spacing I get a cell constant range from 0.238 metre to 0.171 metre. This depends on whether I use the actual spacing of 0.0136 metre or the spacing (on centres) of about 0.0189 metre. The geometric-mean cell constant, using these spacings, is 0.202 metre. Other Methods for Measuring High ResistancesThere are numerous ways to measure high resistances. Typically, insulation testers are adapted for this purpose. For high resistances the applied voltage may range from 100 volts to over 1000 volts. Electrode assemblies can have an increased surface area with a reduced spacing for some high resistance measurements. Electrical shielding and guard circuits are required for the highest resistances. Insulation testers are available from most manufacturers of digital multimeters. Some can measure resistances into the tera-ohm range (1E12 ohms) but only with a completely shielded setup. Using a Multimeter to Measure High ResistancesApart from the insulation testers, a basic digital multimeter and a DC power supply can be used to measure very high resistances. The multimeter voltage ranges typically have a 1E7 ohm input resistance. The lowest voltage range can be used to measure small currents. I do have a meter with a 2.2E10 ohm input resistance on the lowest mV range. This may be useful for some applications or a 1E7 ohm shunt resistor can be added. A 1E7 ohm input resistance UNI-T UT33B multimeter, a 10 volt DC power supply and a series resistance of 1E10 ohms produces a meter reading of 10.0 mV. The measurements can be altered slightly by nearby movements and electrical interference. Using a coaxial cable between the meter and the electrodes should help. Using a 3 volt cell will produce a 3.0 mV reading for a series resistance of 1E10 ohms. For 5E9 ohm series resistance the reading would increase to 6.0 mV. The Resistivity-Probe should give similar results to those obtained with insulation testers, for pure high resistances. For some samples the results might differ, because of the presence of electrolytes. For example the resistance of a Sulphur Superphosphate sample can be measured using two stainless steel chopstick probes. They are spaced 19 mm apart in a plastic cell. The probes are connected in series to a power supply and a multimeter. The current observed is a non-linear function of the applied voltage, as shown below. The points would lie on a straight line from the origin, if the sample was a pure resistance. At 8 volts the current is about 22.5 microamps yielding a resistance of 8 / 2.25E-5 = 3.56E5 ohms and a resistivity of 7.11E4 ohm metre. ![]() Another sample, with 90% sulphur and a gypsum binder formed into pellets, had a high resistance. The sample was loaded with weights totalling 1.6 kg to ensure good probe contacts. The resistance exceeded what my test equipment could measure at about 5E12 ohms, or a resistivity of 1E12 ohm metre. This measurement requires very short leads to avoid any interference. The pellets seem to be incapable of holding charge for a significant time. They were not attracted or repelled by a charged perspex rod. This indicates the resistivity may be measurable with some circuit changes.I ground the pellets and filled a cell to a depth of 2.1 mm. I used my 2.2E10 ohm high impedance voltmeter shunted by my 2.15E9 ohm standard resistor. The voltmeter was connected in series with the cell.
The capacitance of the cell is approximate 30 picofarads. Multiplying this by the observed resistance this gives a time constant of about 9 minutes. The settling time of the measurement was longer. For the pellets I got a resistivity of 2.7E12 ohm metre, using the larger probe based cell. The resistance measurement was 1.4E13 ohms. The cell constant was only 0.2 metre. Note: I have revised this section a few times because the measurements are difficult and there are some interpretation issues. The resistivity of pellet and powder bulk samples should be roughly similar. One is a magnified version of the other to a first approximation. The internal resistivity of a particle or a pellet is essentially the same. Contact resistances between particles or pellets would not add much to any measurement. Measuring the Resistivity of a Memo Cube Paper StackI used a full stack of Memo Cube paper as a test sample with two 52.5 mm diameter electrodes and a 1.6 kilogram weight compressing the electrodes onto the stack. In this case the cell constant is derived from a cylindrical cell matching the diameter of one of the electrodes with a length equal to the thickness of the paper stack.
The Memo Cube resistivity measured with the Resistivity-Probe connected to the electrodes was 1.18E10 ohms x 2.16E-3 /3.55E-2 = 7.18E8 ohm metre. A little time was required to allow the 10 volts applied in the previous measurement to dissipate. The experimental work described here was done at a relative humidity of 70% and a temperature of 20 degrees Celsius. The resistivity of the paper stack will vary greatly when equilibrated to other conditions. The photo below shows the Resistivity-Probe measuring the resistance of a Memo Cube paper stack. To calculate the resistivity of the paper stack, multiply the resistance by the electrode area and divide by the thickness of the paper stack. If the measurements are in metres the resistivity will have a unit of ohm metre. Also shown are weights totalling 1.6 kg and a 2.15E10 ohm reference resistor inside a plastic box with some drying crystals. ![]()
Memo Cube Resistivity
Measurements With Teflon TapeTo test the Resistivity-Probe at higher resistances I used two layers of teflon tape, with a 0.17 mm total thickness covering a 2160 mm^2 tin electrode. The electrodes were connected to the Resistivity-Probe using some clip leads. This setup initially produced a 5 minute integration time. Resistance = (5 x 60 / 43) x 5E9 = 3.49E10 ohms. The cell constant was 2160 / 0.17 = 12700 mm or 12.7 metre. The resistivity of the teflon tape, plus the electrode materials, was 3.75E10 x 12.7 = 4.76E11 ohm metre. Solid teflon has a resistivity around 1E22 ohm metre. On the second day the integration took about took 2 hours. On the third day the integration took about 5 hours. On the fourth day the integration took about 8 hours. The resistance can be calculated as 8 x 3600/43 x 5E9 = 3.35E12 ohms. Multiplying this by 12.7 metre gives a measured resistivity of 4.25E13 ohm metre. Note that this resistivity includes some of the materials used to construct the Resistivity-Probe. I think that during the teflon tape preparation some charges accumulated which caused the probe to misread. Over a few days these charges slowly dissipated. There is no way I can measure the actual 1E22 ohm metre resistivity of teflon. |
JEP Related Links Megger-Guide-to-Insulation-Testing Table of Electrical Resistivity and Conductivity The Basics of Low-Current Probing Example Insulation Tester Measuring gigaohms with a simple multimeter |